If you want to be able to access it externally then yes. I believe if you do use an elastic ip you'll need to modify /etc/openshift/node.conf and set the public_ip to the elastic ip address.
Also make sure that the dns public_hostname in the same file resolves to that IP.

I was able to get OSE in aws using the bash script without much hassle.Have a critical requirement to try some deployment in Origin but this is acting a showstopper

Thanks for the support.

Thanks

Shabna

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